Whoever steps into Europe's new top job as president of the European Council will set the mould. If it is someone of worldwide renown, the presidency will immediately be established as a post of global importance. But if its first occupant is not a household name, the presidency will be doomed as just another of the European Union's confusing plethora of worthy senior positions that are neither valued nor understood outside Brussels.

The key point here is that Europe won't be able to upgrade the job later. If the presidency goes to a politician who lacks fame and charisma, its place will forever be low down in the international pecking order.

Of the half-dozen candidates to become "Europe's president," only Tony Blair needs no introduction anywhere. All the other names in the ring have to be accompanied by a description – the former Finnish this or Austrian that.

Nobody knows whether the current prime ministers of the EU's 27 member countries will choose Blair. There is considerable lingering ill will over his role in the invasion of Iraq, and there is the inconvenient fact that he is from Eurosceptic Britain, and that many on the left view him as a leader whose "third way" was a betrayal of socialism.

But choosing a president for Europe isn't about Blair the man, or about the political records of any of the others who would like the job. It is about the job itself. Europe's problem is that it lacks a clearly identifiable leader. As a result, despite the EU's many successes, it still speaks with too many voices.

This was among the problems that the EU's controversial Lisbon treaty was designed to fix. It is now in the final stages of its long and difficult birth, and by the new year should be bringing new mechanisms to bear to streamline European decision-making. The jewel in its crown is to be the appointment for a 30-month term of a full-time president of the European Council, which groups the heads of EU member governments, along with a foreign policy chief who will be backed by an embryonic EU diplomatic service.

Now that more than two-thirds of Irish voters have reversed their country's earlier opposition to the Lisbon treaty – with only the Czech Republic's Europhobic president, Václav Klaus, holding out against it – the focus is on who will fill these two jobs. And that, in turn, has triggered a round of bitter political squabbling that threatens to negate the entire idea of a much more powerful European voice on the global stage.

The three Benelux countries, along with a few other smaller EU nations, are opposed to the new European president being from a large nation. And there are also those who fear that a political heavyweight in the job might eclipse the EU Commission's president, former Portuguese prime minister José Manuel Barroso, who has just been confirmed for a second five-year term, and devalue the role of the foreign policy chief whose authority Lisbon is due to beef up.

These are specious arguments. The EU's external relations involve two different types of politics. The first is the politics of world theatre, where a political figure of global stature could do much to raise the EU's profile and ensure that it has a major say in re-ordering the post-crisis global economic rulebook. The second is the politics of detail, where the new foreign policy chief's role is to create a single EU stance on the wide range of issues about which European governments still have wildly different national positions.

Europe has an international image problem that in part stems from a complex institutional structure that non-EU countries find baffling. It is over-represented at G20 world summits, for instance, but the presence of four European national leaders, plus EU representatives such as Barroso, weakens rather than strengthens its political weight. The same is true of other global bodiessuch as the World Bank and the International Monetary Fund.

The result is that Europe's achievements in recent years – its expansion to create a single economic market of 500 million people and its creation of the euro as a currency that challenges the dollar – are not accompanied by a significantly greater global standing. World leaders from Barack Obama to Hu Jintao address themselves to Berlin, Paris, and London, rather than to Brussels. The result is that EU policy proposals that could do much to advance the economic and geopolitical interests of Europeans are not as influential as they could be.

The text of the Lisbon treaty is studiously vague in its job description of the president's role – an approach that prevented trouble for treaty's framers, but merely postponed disagreement. The real argument now taking place between Europe's national governments is about the authority that the EU's president should have. The risk is that Europe's squabbling politicians will opt for a figurehead and miss this golden opportunity to create a global leader.